Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x-8y &= 2 \\ 2x+y &= 2\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {-2x+2}$ Substitute this expression for $y$ in the first equation. $-4x-8({-2x + 2}) = 2$ $-4x + 16x - 16 = 2$ Simplify by combining terms, then solve for $x$ $12x - 16 = 2$ $12x = 18$ $x = \dfrac{3}{2}$ Substitute $\dfrac{3}{2}$ for $x$ back into the top equation. $-4( \dfrac{3}{2})-8y = 2$ $-6-8y = 2$ $-8y = 8$ $y = -1$ The solution is $\enspace x = \dfrac{3}{2}, \enspace y = -1$.